Medium eg:
7x64
280
.270 Win (I know more like 6.8x64 in terms of the metric system but I think ballistically so close out on an off the shelf sporter with factory ammo we're splitting hairs)

Hot:
7mm Magnums - Various.

Sure that's fine. Things even out when you compare commercial loads to hand loads, hot to mild etc.
imho within certain limits any of the standard cartridges will work fine on American game and most can be very good target rounds.
The rifle and the shooter have more to do with results than cartridge,